Non-linear massive gravity as a gravitational σ-model
1 Department of Physics, Faculty of Science, Tokyo University of Science - 1-3, Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan
2 State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Science Beijing 100190, PRC
Received: 31 March 2016
Accepted: 17 August 2016
We show the direct analogy between the ghost-free non-linear formulation of massive gravity and the standard σ-models well understood in the literature. This issue explains why there are two non-trivial family of solutions for the spherically symmetric case inside the non-linear massive gravity formulations with two free parameters α and β. In general, the case has a single physical vacuum state. On the other hand, the case contains a natural vacuum degeneracy. This is in perfect analogy with the σ-model for scalar fields where depending on the values taken by the parameters of the theory the vacuum can be single or degenerate.
PACS: 11.15.Ex – Spontaneous breaking of gauge symmetries / 14.70.Kv – Gravitons / 11.15.-q – Gauge field theories
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